Solve for $p$, $ \dfrac{3p - 2}{8p - 4} = \dfrac{1}{12p - 6} + \dfrac{1}{4p - 2} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8p - 4$ $12p - 6$ and $4p - 2$ The common denominator is $24p - 12$ To get $24p - 12$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{3p - 2}{8p - 4} \times \dfrac{3}{3} = \dfrac{9p - 6}{24p - 12} $ To get $24p - 12$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{1}{12p - 6} \times \dfrac{2}{2} = \dfrac{2}{24p - 12} $ To get $24p - 12$ in the denominator of the third term, multiply it by $\frac{6}{6}$ $ \dfrac{1}{4p - 2} \times \dfrac{6}{6} = \dfrac{6}{24p - 12} $ This give us: $ \dfrac{9p - 6}{24p - 12} = \dfrac{2}{24p - 12} + \dfrac{6}{24p - 12} $ If we multiply both sides of the equation by $24p - 12$ , we get: $ 9p - 6 = 2 + 6$ $ 9p - 6 = 8$ $ 9p = 14 $ $ p = \dfrac{14}{9}$